{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:SN7EZ5N2AHA7DCBRORDPU56YR3","short_pith_number":"pith:SN7EZ5N2","canonical_record":{"source":{"id":"2301.04390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T10:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"08cd3fc4eb1285df4320b4e5688ce410e6599188497e14946590fbdabb81ef4b","abstract_canon_sha256":"50d64c569e27681217d3fb6136e344d8849808f6ce5320801c78bb3cb3c8dfb7"},"schema_version":"1.0"},"canonical_sha256":"937e4cf5ba01c1f188317446fa77d88ed54eda54645b61d8d9e822c8b28ae08f","source":{"kind":"arxiv","id":"2301.04390","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04390","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04390v1","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04390","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_12","alias_value":"SN7EZ5N2AHA7","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"SN7EZ5N2AHA7DCBR","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"SN7EZ5N2","created_at":"2026-07-05T05:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:SN7EZ5N2AHA7DCBRORDPU56YR3","target":"record","payload":{"canonical_record":{"source":{"id":"2301.04390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T10:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"08cd3fc4eb1285df4320b4e5688ce410e6599188497e14946590fbdabb81ef4b","abstract_canon_sha256":"50d64c569e27681217d3fb6136e344d8849808f6ce5320801c78bb3cb3c8dfb7"},"schema_version":"1.0"},"canonical_sha256":"937e4cf5ba01c1f188317446fa77d88ed54eda54645b61d8d9e822c8b28ae08f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:32:25.049379Z","signature_b64":"sq9W10MMh2zvsclom4R5dTjcAAqmqQKMaunaB8fc143fmYNfAS/PV88LhrxuFLDrjedO3Thg8yIDph9TowxEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937e4cf5ba01c1f188317446fa77d88ed54eda54645b61d8d9e822c8b28ae08f","last_reissued_at":"2026-07-05T05:32:25.048956Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:32:25.048956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.04390","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:32:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zz9yYyTwBIdVlcOU739HloggRdvA0kGuzGzIrATQ3ipfYxrzolMX2THiSqW2GV2hCLekB39fbaYfMPNc0ay4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:07:41.335558Z"},"content_sha256":"0f409536aa216682a6be95e35c7d272ec63ac51f93f1547416d961a518e10514","schema_version":"1.0","event_id":"sha256:0f409536aa216682a6be95e35c7d272ec63ac51f93f1547416d961a518e10514"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:SN7EZ5N2AHA7DCBRORDPU56YR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The typical size of character and zeta sums is $o(\\sqrt{x})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adam J. Harper","submitted_at":"2023-01-11T10:28:14Z","abstract_excerpt":"We prove conjecturally sharp upper bounds for the Dirichlet character moments $\\frac{1}{r-1} \\sum_{\\chi \\; \\text{mod} \\; r} |\\sum_{n \\leq x} \\chi(n)|^{2q}$, where $r$ is a large prime, $1 \\leq x \\leq r$, and $0 \\leq q \\leq 1$ is real. In particular, if both $x$ and $r/x$ tend to infinity with $r$ then $\\frac{1}{r-1} \\sum_{\\chi \\; \\text{mod} \\; r} |\\sum_{n \\leq x} \\chi(n)| = o(\\sqrt{x})$, and so the sums $\\sum_{n \\leq x} \\chi(n)$ typically exhibit \"better than squareroot cancellation\". We prove analogous better than squareroot bounds for the moments $\\frac{1}{T} \\int_{0}^{T} |\\sum_{n \\leq x} n^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04390","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.04390/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:32:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PUGtp4UqEbDk47yPudtSBy5YSwywQjI6H1wO2f94K5+q8/UQVBnkjKMS7sjsiHaQIOKjICD0KGgx8LpvvMsJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:07:41.336055Z"},"content_sha256":"b68edc264ed2652044a4c86cfe15f2d84a8b0f41548c2b76a5f1c4e80d08ce60","schema_version":"1.0","event_id":"sha256:b68edc264ed2652044a4c86cfe15f2d84a8b0f41548c2b76a5f1c4e80d08ce60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/bundle.json","state_url":"https://pith.science/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T19:07:41Z","links":{"resolver":"https://pith.science/pith/SN7EZ5N2AHA7DCBRORDPU56YR3","bundle":"https://pith.science/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/bundle.json","state":"https://pith.science/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SN7EZ5N2AHA7DCBRORDPU56YR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SN7EZ5N2AHA7DCBRORDPU56YR3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"50d64c569e27681217d3fb6136e344d8849808f6ce5320801c78bb3cb3c8dfb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T10:28:14Z","title_canon_sha256":"08cd3fc4eb1285df4320b4e5688ce410e6599188497e14946590fbdabb81ef4b"},"schema_version":"1.0","source":{"id":"2301.04390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04390","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04390v1","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04390","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_12","alias_value":"SN7EZ5N2AHA7","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"SN7EZ5N2AHA7DCBR","created_at":"2026-07-05T05:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"SN7EZ5N2","created_at":"2026-07-05T05:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:b68edc264ed2652044a4c86cfe15f2d84a8b0f41548c2b76a5f1c4e80d08ce60","target":"graph","created_at":"2026-07-05T05:32:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2301.04390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove conjecturally sharp upper bounds for the Dirichlet character moments $\\frac{1}{r-1} \\sum_{\\chi \\; \\text{mod} \\; r} |\\sum_{n \\leq x} \\chi(n)|^{2q}$, where $r$ is a large prime, $1 \\leq x \\leq r$, and $0 \\leq q \\leq 1$ is real. In particular, if both $x$ and $r/x$ tend to infinity with $r$ then $\\frac{1}{r-1} \\sum_{\\chi \\; \\text{mod} \\; r} |\\sum_{n \\leq x} \\chi(n)| = o(\\sqrt{x})$, and so the sums $\\sum_{n \\leq x} \\chi(n)$ typically exhibit \"better than squareroot cancellation\". We prove analogous better than squareroot bounds for the moments $\\frac{1}{T} \\int_{0}^{T} |\\sum_{n \\leq x} n^","authors_text":"Adam J. Harper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T10:28:14Z","title":"The typical size of character and zeta sums is $o(\\sqrt{x})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04390","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0f409536aa216682a6be95e35c7d272ec63ac51f93f1547416d961a518e10514","target":"record","created_at":"2026-07-05T05:32:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"50d64c569e27681217d3fb6136e344d8849808f6ce5320801c78bb3cb3c8dfb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-01-11T10:28:14Z","title_canon_sha256":"08cd3fc4eb1285df4320b4e5688ce410e6599188497e14946590fbdabb81ef4b"},"schema_version":"1.0","source":{"id":"2301.04390","kind":"arxiv","version":1}},"canonical_sha256":"937e4cf5ba01c1f188317446fa77d88ed54eda54645b61d8d9e822c8b28ae08f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"937e4cf5ba01c1f188317446fa77d88ed54eda54645b61d8d9e822c8b28ae08f","first_computed_at":"2026-07-05T05:32:25.048956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:32:25.048956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sq9W10MMh2zvsclom4R5dTjcAAqmqQKMaunaB8fc143fmYNfAS/PV88LhrxuFLDrjedO3Thg8yIDph9TowxEBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:32:25.049379Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.04390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f409536aa216682a6be95e35c7d272ec63ac51f93f1547416d961a518e10514","sha256:b68edc264ed2652044a4c86cfe15f2d84a8b0f41548c2b76a5f1c4e80d08ce60"],"state_sha256":"481fbe99e4c5190a2d1c42322bc0a657a546b7a57ecd32aa1de1d0ad6e669b11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YN4Tf65vHA0r71cobuGaE3uF6OAF0OhW+6eiPzXb2oIWQ4tJofG52eTJd6YiqtZ9PnJPx/m6ufKXgfubW0XZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:07:41.341751Z","bundle_sha256":"61bf115af895f8ac80984659a4c546070b23b2ddb6e445425275c3e4e8a34e01"}}